A172339 Triangle t(n,k) read by rows: fibonomial ratios c(n)/(c(k)*c(n-k)) where c are partial products of a generalized Fibonacci sequence with multiplier m=3.

1, 1, 1, 1, 3, 1, 1, 10, 10, 1, 1, 33, 110, 33, 1, 1, 109, 1199, 1199, 109, 1, 1, 360, 13080, 43164, 13080, 360, 1, 1, 1189, 142680, 1555212, 1555212, 142680, 1189, 1, 1, 3927, 1556401, 56030436, 185070228, 56030436, 1556401, 3927, 1, 1, 12970, 16977730

Offset

0,5

Comments

Build with the recipe of A010048 (m=1) and A099927 (m=2).

Start from the generalized Fibonacci sequence A006190 and its partial products c(n) = 1, 1, 3, 30, 990, 107910, 38847600, 46189796400,... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 5, 22, 178, 2618, 70046, 3398164, 300251758, 48114604076,

14041125439724,...

Links

Table of n, a(n) for n=0..47.

Example

1;
1, 1;
1, 3, 1;
1, 10, 10, 1;
1, 33, 110, 33, 1;
1, 109, 1199, 1199, 109, 1;
1, 360, 13080, 43164, 13080, 360, 1;
1, 1189, 142680, 1555212, 1555212, 142680, 1189, 1;
1, 3927, 1556401, 56030436, 185070228, 56030436, 1556401, 3927, 1;
1, 12970, 16977730, 2018652097, 22021659240, 22021659240, 2018652097, 16977730, 12970, 1;

Mathematica

Clear[f, c, a, t];
f[0, a_] := 0; f[1, a_] := 1;
f[n_, a_] := f[n, a] = a*f[n - 1, a] + f[n - 2, a];
c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];
t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);
Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];
Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]

Crossrefs

Cf. A010048 (m=1), A099927 (m=2), A034802 (m=4), A172342 (m=5).

Sequence in context: A261215 A176157 A176156 * A342972 A060540 A087647

Adjacent sequences: A172336 A172337 A172338 * A172340 A172341 A172342

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Feb 01 2010

Status

approved